-------------------------------------------------------------------------------------------
      name:  <unnamed>
       log:  ~\PG_DataFile\pg_log.log
  log type:  text
 opened on:   1 Apr 2021, 23:18:11

. 
. **************
. *** Coding ***
. **************
. 
. *** Treatment conditions
. sort sessionid period group subject

. recode treatment 1=2 2=3 3=1, gen(treatment2)
(1944 differences between treatment and treatment2)

. drop treatment

. rename treatment2 treatment

. label define treatment_lb 2 "Gr.Major." 3 "Gr.Benefit" 1 "No Info" 

. label values treatment treatment_lb

. label var treatment "Treatment"

. 
. *** Ind. utility from PG (Dummy, 1=pos., 0=neg.)
. gen     ind_util_pos = .
(1,944 missing values generated)

. replace ind_util_pos = 1 if  netpay== 8
(162 real changes made)

. replace ind_util_pos = 1 if  netpay== 3
(810 real changes made)

. replace ind_util_pos = 0 if  netpay==-3
(810 real changes made)

. replace ind_util_pos = 0 if  netpay==-8
(162 real changes made)

. label var ind_util_pos "Ind. Utility"

. label define ind_util_pos_lb 1 "Ind.U. Pos." 0 "Ind.U. Neg." 

. label values ind_util_pos ind_util_pos_lb

. 
. *** Group majority (Dummy, 1= pro PG, 0 = contra PG)
. gen gr_maj_pos = .
(1,944 missing values generated)

. replace gr_maj_pos = 1 if majority==1
(972 real changes made)

. replace gr_maj_pos = 0 if majority==0
(972 real changes made)

. label var gr_maj_pos "Group Majority"

. label define gr_maj_pos_lb 1 "Pro PG" 0 "Contra PG" 

. label values gr_maj_pos gr_maj_pos_lb

. 
. *** Group Benefit (Dummy, 1=pos., 0=neg.)
. gen     gr_util_pos = .
(1,944 missing values generated)

. replace gr_util_pos = 1 if  networth==  3
(486 real changes made)

. replace gr_util_pos = 1 if  networth==  2
(486 real changes made)

. replace gr_util_pos = 0 if  networth== -2
(486 real changes made)

. replace gr_util_pos = 0 if  networth== -3
(486 real changes made)

. label var gr_util_pos "Group Benefit"

. label define gr_util_pos_lb 1 "Pos." 0 "Neg." 

. label values gr_util_pos gr_util_pos_lb

. 
. *** Rational procedural choice MV vs. Delegation (for T2 and T3)
. gen rat_MV = .
(1,944 missing values generated)

. replace rat_MV = 1 if gr_maj_pos==1 & ind_util_pos==1 & treatment==2
(276 real changes made)

. replace rat_MV = 1 if gr_maj_pos==0 & ind_util_pos==0 & treatment==2
(276 real changes made)

. replace rat_MV = 0 if gr_maj_pos==1 & ind_util_pos==0 & treatment==2
(138 real changes made)

. replace rat_MV = 0 if gr_maj_pos==0 & ind_util_pos==1 & treatment==2
(138 real changes made)

. replace rat_MV = 0 if gr_util_pos==1 & ind_util_pos==1 & treatment==3
(135 real changes made)

. replace rat_MV = 0 if gr_util_pos==0 & ind_util_pos==0 & treatment==3
(135 real changes made)

. replace rat_MV = 1 if gr_util_pos==1 & ind_util_pos==0 & treatment==3
(135 real changes made)

. replace rat_MV = 1 if gr_util_pos==0 & ind_util_pos==1 & treatment==3
(135 real changes made)

. label var rat_MV "Rat. procedure choice"

. label define rat_MV_lb 1 "MV" 0 "Delegate" 

. label values rat_MV rat_MV_lb

. 
. *** Rational procedural choice MV vs. Delegation (by Treatment) [PLACEBO for T1 & T2]
. gen rat_MVp1 = .
(1,944 missing values generated)

. replace rat_MVp1 = 1 if gr_maj_pos==1 & ind_util_pos==1 & treatment==2
(276 real changes made)

. replace rat_MVp1 = 1 if gr_maj_pos==0 & ind_util_pos==0 & treatment==2
(276 real changes made)

. replace rat_MVp1 = 0 if gr_maj_pos==1 & ind_util_pos==0 & treatment==2
(138 real changes made)

. replace rat_MVp1 = 0 if gr_maj_pos==0 & ind_util_pos==1 & treatment==2
(138 real changes made)

. replace rat_MVp1 = 1 if gr_maj_pos==1 & ind_util_pos==1 & treatment==1
(192 real changes made)

. replace rat_MVp1 = 1 if gr_maj_pos==0 & ind_util_pos==0 & treatment==1
(192 real changes made)

. replace rat_MVp1 = 0 if gr_maj_pos==1 & ind_util_pos==0 & treatment==1
(96 real changes made)

. replace rat_MVp1 = 0 if gr_maj_pos==0 & ind_util_pos==1 & treatment==1
(96 real changes made)

. label var rat_MVp1 "Rat. procedure choice"

. label define rat_MVp1_lb 1 "MV" 0 "Delegate" 

. label values rat_MVp1 rat_MVp1_lb

. 
. *** Rational procedural choice MV vs. Delegation (by Treatment) [PLACEBO for T1 & T3]
. gen rat_MVp2 = .
(1,944 missing values generated)

. replace rat_MVp2 = 0 if gr_util_pos==1 & ind_util_pos==1 & treatment==3
(135 real changes made)

. replace rat_MVp2 = 0 if gr_util_pos==0 & ind_util_pos==0 & treatment==3
(135 real changes made)

. replace rat_MVp2 = 1 if gr_util_pos==1 & ind_util_pos==0 & treatment==3
(135 real changes made)

. replace rat_MVp2 = 1 if gr_util_pos==0 & ind_util_pos==1 & treatment==3
(135 real changes made)

. replace rat_MVp2 = 0 if gr_util_pos==1 & ind_util_pos==1 & treatment==1
(144 real changes made)

. replace rat_MVp2 = 0 if gr_util_pos==0 & ind_util_pos==0 & treatment==1
(144 real changes made)

. replace rat_MVp2 = 1 if gr_util_pos==1 & ind_util_pos==0 & treatment==1
(144 real changes made)

. replace rat_MVp2 = 1 if gr_util_pos==0 & ind_util_pos==1 & treatment==1
(144 real changes made)

. label var rat_MVp2 "Rat. procedure choice"

. label define rat_MVp2_lb 1 "MV" 0 "Delegate" 

. label values rat_MVp2 rat_MVp2_lb

. 
. *** Rational procedural choice: EU(MV)
. gen     rat_MV_cat = .
(1,944 missing values generated)

. * Netpay is positive, and MV makes it more likely to get it --> expected net gain from MV
>  positive
. replace rat_MV_cat = (1-2/3)*netpay     if gr_maj_pos==1  & ind_util_pos==1 & treatment==
> 2
(276 real changes made)

. * Netpay is negative, and MV makes it more likely to avoid it --> expected net gain from 
> MV positive
. replace rat_MV_cat = (-1)*1/3*netpay    if gr_maj_pos==0  & ind_util_pos==0 & treatment==
> 2
(276 real changes made)

. * Netpay is negative and MV makes it more likely to suffer from it --> expected net gain 
> from MV negative
. replace rat_MV_cat = (1-0.5)*netpay     if gr_maj_pos==1  & ind_util_pos==0 & treatment==
> 2
(138 real changes made)

. * Netpay is positive and MV makes it more likely to miss it --> expected net gain from MV
>  negative
. replace rat_MV_cat = (-1)*0.5*netpay    if gr_maj_pos==0  & ind_util_pos==1 & treatment==
> 2
(138 real changes made)

. 
. * Netpay is positive, and MV makes it more likely to get it --> expected net gain from MV
>  positive
. replace rat_MV_cat = 2/3*netpay         if gr_util_pos==0  & ind_util_pos==1 & treatment=
> =3
(135 real changes made)

. * Netpay is negative, and MV makes it more likely to avoid it --> expected net gain from 
> MV positive
. replace rat_MV_cat = (1/3-1)*netpay     if gr_util_pos==1  & ind_util_pos==0 & treatment=
> =3
(135 real changes made)

. * Netpay is negative and MV makes it more likely to suffer from it --> expected net gain 
> from MV negative
. replace rat_MV_cat = 1/4*netpay                 if gr_util_pos==0  & ind_util_pos==0 & tr
> eatment==3
(135 real changes made)

. * Netpay is positive and MV makes it more likely to miss it --> expected net gain from MV
>  negative
. replace rat_MV_cat = (3/4-1)*netpay     if gr_util_pos==1  & ind_util_pos==1 & treatment=
> =3
(135 real changes made)

. 
. 
. *** Rational procedural choice: EU(MV) for T2 and T3 [PLACEBO T1 & T2]
. gen     rat_MV_catp1 = .
(1,944 missing values generated)

. * Netpay is positive, and MV makes it more likely to get it --> expected net gain from MV
>  positive
. replace rat_MV_catp1 = (1-2/3)*netpay     if gr_maj_pos==1  & ind_util_pos==1 & treatment
> ==2
(276 real changes made)

. * Netpay is negative, and MV makes it more likely to avoid it --> expected net gain from 
> MV positive
. replace rat_MV_catp1 = (-1)*1/3*netpay          if gr_maj_pos==0  & ind_util_pos==0 & tre
> atment==2
(276 real changes made)

. * Netpay is negative and MV makes it more likely to suffer from it --> expected net gain 
> from MV negative
. replace rat_MV_catp1 = (1-0.5)*netpay     if gr_maj_pos==1  & ind_util_pos==0 & treatment
> ==2
(138 real changes made)

. * Netpay is positive and MV makes it more likely to miss it --> expected net gain from MV
>  negative
. replace rat_MV_catp1 = (-1)*0.5*netpay  if gr_maj_pos==0  & ind_util_pos==1 & treatment==
> 2
(138 real changes made)

. * Netpay is positive, and MV makes it more likely to get it --> expected net gain from MV
>  positive
. replace rat_MV_catp1 = (1-2/3)*netpay     if gr_maj_pos==1  & ind_util_pos==1 & treatment
> ==1
(192 real changes made)

. * Netpay is negative, and MV makes it more likely to avoid it --> expected net gain from 
> MV positive
. replace rat_MV_catp1 = (-1)*1/3*netpay          if gr_maj_pos==0  & ind_util_pos==0 & tre
> atment==1
(192 real changes made)

. * Netpay is negative and MV makes it more likely to suffer from it --> expected net gain 
> from MV negative
. replace rat_MV_catp1 = (1-0.5)*netpay     if gr_maj_pos==1  & ind_util_pos==0 & treatment
> ==1
(96 real changes made)

. * Netpay is positive and MV makes it more likely to miss it --> expected net gain from MV
>  negative
. replace rat_MV_catp1 = (-1)*0.5*netpay  if gr_maj_pos==0  & ind_util_pos==1 & treatment==
> 1
(96 real changes made)

. 
. *** Rational procedural choice: EU(MV) for T2 and T3 [PLACEBO T1 & T3]
. gen     rat_MV_catp2 = .
(1,944 missing values generated)

. * Netpay is positive, and MV makes it more likely to get it --> expected net gain from MV
>  positive
. replace rat_MV_catp2 = 2/3*netpay       if gr_util_pos==0  & ind_util_pos==1 & treatment=
> =3
(135 real changes made)

. * Netpay is negative, and MV makes it more likely to avoid it --> expected net gain from 
> MV positive
. replace rat_MV_catp2 = (1/3-1)*netpay           if gr_util_pos==1  & ind_util_pos==0 & tr
> eatment==3
(135 real changes made)

. * Netpay is negative and MV makes it more likely to suffer from it --> expected net gain 
> from MV negative
. replace rat_MV_catp2 = 1/4*netpay               if gr_util_pos==0  & ind_util_pos==0 & tr
> eatment==3
(135 real changes made)

. * Netpay is positive and MV makes it more likely to miss it --> expected net gain from MV
>  negative
. replace rat_MV_catp2 = (3/4-1)*netpay   if gr_util_pos==1  & ind_util_pos==1 & treatment=
> =3
(135 real changes made)

. * Netpay is positive, and MV makes it more likely to get it --> expected net gain from MV
>  positive
. replace rat_MV_catp2 = 2/3*netpay       if gr_util_pos==0  & ind_util_pos==1 & treatment=
> =1
(144 real changes made)

. * Netpay is negative, and MV makes it more likely to avoid it --> expected net gain from 
> MV positive
. replace rat_MV_catp2 = (1/3-1)*netpay           if gr_util_pos==1  & ind_util_pos==0 & tr
> eatment==1
(144 real changes made)

. * Netpay is negative and MV makes it more likely to suffer from it --> expected net gain 
> from MV negative
. replace rat_MV_catp2 = 1/4*netpay               if gr_util_pos==0  & ind_util_pos==0 & tr
> eatment==1
(144 real changes made)

. * Netpay is positive and MV makes it more likely to miss it --> expected net gain from MV
>  negative
. replace rat_MV_catp2 = (3/4-1)*netpay   if gr_util_pos==1  & ind_util_pos==1 & treatment=
> =1
(144 real changes made)

. 
. 
. *****************
. **** Figure 1 ***
. *****************
. 
. tsset id period
       panel variable:  id (strongly balanced)
        time variable:  period, 1 to 12
                delta:  1 unit

. fvset base 1 treatment

. xtlogit decisionprocedure               i.treatment     i.period                , re vce(
> robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -1309.3016  
Iteration 1:   log pseudolikelihood =  -1289.762  
Iteration 2:   log pseudolikelihood = -1289.7487  
Iteration 3:   log pseudolikelihood = -1289.7487  

Fitting full model:

tau =  0.0     log pseudolikelihood = -1289.7487
tau =  0.1     log pseudolikelihood = -1274.6813
tau =  0.2     log pseudolikelihood = -1267.6601
tau =  0.3     log pseudolikelihood = -1265.9193
tau =  0.4     log pseudolikelihood = -1268.2691

Iteration 0:   log pseudolikelihood =  -1265.919  
Iteration 1:   log pseudolikelihood = -1265.6629  
Iteration 2:   log pseudolikelihood = -1265.6626  
Iteration 3:   log pseudolikelihood = -1265.6626  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,944
Group variable: id                              Number of groups  =        162

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(13)     =      29.54
Log pseudolikelihood  = -1265.6626              Prob > chi2       =     0.0055

                                        (Std. Err. adjusted for 162 clusters in id)
-----------------------------------------------------------------------------------
                  |               Robust
decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
        treatment |
       Gr.Major.  |   -.029104    .178831    -0.16   0.871    -.3796064    .3213984
      Gr.Benefit  |   -.566615   .1951877    -2.90   0.004    -.9491759   -.1840541
                  |
           period |
               2  |  -.2193992   .2426029    -0.90   0.366    -.6948921    .2560938
               3  |   .1952038   .2387265     0.82   0.414    -.2726915    .6630992
               4  |   .3965731   .2537144     1.56   0.118    -.1006979    .8938441
               5  |   .1670155    .249891     0.67   0.504    -.3227618    .6567928
               6  |  -2.06e-17    .238113    -0.00   1.000    -.4666929    .4666929
               7  |   .3672998   .2483767     1.48   0.139    -.1195095    .8541091
               8  |   .3093024   .2436171     1.27   0.204    -.1681783    .7867831
               9  |   .3382133   .2460332     1.37   0.169    -.1440028    .8204294
              10  |   .3965731   .2571082     1.54   0.123    -.1073496    .9004959
              11  |   .4856321   .2506069     1.94   0.053    -.0055483    .9768126
              12  |   .2805563   .2454196     1.14   0.253    -.2004573    .7615699
                  |
            _cons |   .3878681   .2051339     1.89   0.059     -.014187    .7899232
------------------+----------------------------------------------------------------
         /lnsig2u |  -.8826749   .2810867                     -1.433595   -.3317552
------------------+----------------------------------------------------------------
          sigma_u |   .6431756    .090394                      .4883136    .8471499
              rho |   .1116971   .0278897                      .0675818    .1790786
-----------------------------------------------------------------------------------

. est store m1

. margins  treatment

Predictive margins                              Number of obs     =      1,944
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   treatment |
    No Info  |   .6360301    .031477    20.21   0.000     .5743363    .6977238
  Gr.Major.  |   .6298702   .0211722    29.75   0.000     .5883734     .671367
 Gr.Benefit  |   .5108971   .0289596    17.64   0.000     .4541373     .567657
------------------------------------------------------------------------------

. marginsplot,  ytitle("Pr(MV)") recast(scatter)

  Variables that uniquely identify margins: treatment

. graph save fig1.gph, replace
(note: file fig1.gph not found)
(file fig1.gph saved)

. 
. *********************
. **** Figure 2a/b ****
. *********************
. 
. **** DUMMY Group Majority & Benefit Treatments: Rational prediction of procedrual choice
. xtlogit decisionprocedure i.rat_MV        i.period if treatment!=1 , re vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -929.13639  
Iteration 1:   log pseudolikelihood = -832.16611  
Iteration 2:   log pseudolikelihood = -831.84257  
Iteration 3:   log pseudolikelihood =  -831.8425  

Fitting full model:

tau =  0.0     log pseudolikelihood =  -831.8425
tau =  0.1     log pseudolikelihood =  -822.7499
tau =  0.2     log pseudolikelihood = -818.23189
tau =  0.3     log pseudolikelihood = -816.99097
tau =  0.4     log pseudolikelihood = -818.44353

Iteration 0:   log pseudolikelihood = -816.99091  
Iteration 1:   log pseudolikelihood = -816.52873  
Iteration 2:   log pseudolikelihood =  -816.5284  
Iteration 3:   log pseudolikelihood =  -816.5284  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,368
Group variable: id                              Number of groups  =        114

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(12)     =      50.04
Log pseudolikelihood  =  -816.5284              Prob > chi2       =     0.0000

                                        (Std. Err. adjusted for 114 clusters in id)
-----------------------------------------------------------------------------------
                  |               Robust
decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
           rat_MV |
              MV  |   1.694758   .2565599     6.61   0.000     1.191909    2.197606
                  |
           period |
               2  |   -.114716   .2976969    -0.39   0.700    -.6981912    .4687592
               3  |   .2544872   .2955246     0.86   0.389    -.3247303    .8337047
               4  |   .2512379   .3080264     0.82   0.415    -.3524827    .8549585
               5  |   .2484748   .3193271     0.78   0.436    -.3773949    .8743445
               6  |   .1213597   .3191841     0.38   0.704    -.5042297     .746949
               7  |   .3932656   .3191136     1.23   0.218    -.2321855    1.018717
               8  |   .2682321   .2936718     0.91   0.361    -.3073541    .8438182
               9  |   .2301863   .3008719     0.77   0.444    -.3595118    .8198845
              10  |   .1674318   .3103537     0.54   0.590    -.4408502    .7757139
              11  |   .3134068   .3129914     1.00   0.317     -.300045    .9268587
              12  |   .1802261   .2945355     0.61   0.541    -.3970529    .7575051
                  |
            _cons |  -.8009731   .2674151    -3.00   0.003    -1.325097   -.2768492
------------------+----------------------------------------------------------------
         /lnsig2u |  -.8192583   .3618982                     -1.528566   -.1099509
------------------+----------------------------------------------------------------
          sigma_u |   .6638964   .1201315                      .4656678    .9465084
              rho |    .118146   .0377053                      .0618375    .2140307
-----------------------------------------------------------------------------------

. est store m2a 

. margins  rat_MV

Predictive margins                              Number of obs     =      1,368
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      rat_MV |
   Delegate  |   .3654797   .0342485    10.67   0.000     .2983538    .4326056
         MV  |   .7290125    .026485    27.53   0.000     .6771029     .780922
------------------------------------------------------------------------------

. marginsplot,  yline(.6361708, lpattern(solid)) yline(.575639 , lpattern(dash)) yline(.696
> 7027, lpattern(dash)) ytitle("Pr(MV)") xtitle(" ")  title("A")

  Variables that uniquely identify margins: rat_MV

. graph save fig2a.gph, replace
(note: file fig2a.gph not found)
(file fig2a.gph saved)

. 
. **** METRIC Group Majority & Benefit Treatments: Rational prediction of procedrual choice
>  
. xtlogit decisionprocedure c.rat_MV_cat        i.period if treatment!=1 , re vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -929.13639  
Iteration 1:   log pseudolikelihood =  -856.5885  
Iteration 2:   log pseudolikelihood = -856.34283  
Iteration 3:   log pseudolikelihood = -856.34279  

Fitting full model:

tau =  0.0     log pseudolikelihood = -856.34279
tau =  0.1     log pseudolikelihood = -843.48695
tau =  0.2     log pseudolikelihood = -836.35748
tau =  0.3     log pseudolikelihood = -833.16266
tau =  0.4     log pseudolikelihood = -833.06264
tau =  0.5     log pseudolikelihood = -835.78225

Iteration 0:   log pseudolikelihood = -833.06825  
Iteration 1:   log pseudolikelihood = -831.34463  
Iteration 2:   log pseudolikelihood = -831.34308  
Iteration 3:   log pseudolikelihood = -831.34308  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,368
Group variable: id                              Number of groups  =        114

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(12)     =      45.59
Log pseudolikelihood  = -831.34308              Prob > chi2       =     0.0000

                                        (Std. Err. adjusted for 114 clusters in id)
-----------------------------------------------------------------------------------
                  |               Robust
decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
       rat_MV_cat |    .424415   .0683132     6.21   0.000     .2905236    .5583063
                  |
           period |
               2  |  -.0336931    .293021    -0.11   0.908    -.6080037    .5406175
               3  |   .4084453   .2886233     1.42   0.157    -.1572459    .9741365
               4  |   .3177723   .2975933     1.07   0.286    -.2654998    .9010445
               5  |   .2436552   .3065801     0.79   0.427    -.3572308    .8445412
               6  |   .1146327   .3075246     0.37   0.709    -.4881045    .7173699
               7  |   .4726304   .3092198     1.53   0.126    -.1334293     1.07869
               8  |   .4142761   .2934916     1.41   0.158    -.1609568     .989509
               9  |   .4681462   .3085652     1.52   0.129    -.1366305    1.072923
              10  |   .3868075   .3134469     1.23   0.217    -.2275373    1.001152
              11  |   .4492358   .3087026     1.46   0.146    -.1558102    1.054282
              12  |   .4162824   .2950021     1.41   0.158    -.1619111     .994476
                  |
            _cons |   .0947043   .2118059     0.45   0.655    -.3204276    .5098362
------------------+----------------------------------------------------------------
         /lnsig2u |  -.4961105    .316629                     -1.116692    .1244709
------------------+----------------------------------------------------------------
          sigma_u |   .7803168   .1235355                      .5721547    1.064213
              rho |   .1561763    .041727                      .0905005    .2560928
-----------------------------------------------------------------------------------

. est store m2b

. margins, at(rat_MV_cat=(-4 -2 -1.5 -.75 1 2))  

Predictive margins                              Number of obs     =      1,368
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)

1._at        : rat_MV_cat      =          -4

2._at        : rat_MV_cat      =          -2

3._at        : rat_MV_cat      =        -1.5

4._at        : rat_MV_cat      =        -.75

5._at        : rat_MV_cat      =           1

6._at        : rat_MV_cat      =           2

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .2408771   .0447049     5.39   0.000     .1532571    .3284971
          2  |   .4027788   .0331955    12.13   0.000     .3377168    .4678407
          3  |   .4482977   .0288096    15.56   0.000     .3918319    .5047635
          4  |   .5178516    .023059    22.46   0.000     .4726567    .5630465
          5  |   .6736962   .0233064    28.91   0.000     .6280165     .719376
          6  |   .7508893   .0279905    26.83   0.000     .6960289    .8057497
------------------------------------------------------------------------------

. marginsplot, yline(.6361708, lpattern(solid)) yline(.575639 , lpattern(dash)) yline(.6967
> 027, lpattern(dash)) ytitle("Pr(MV)") xtitle("EU(MV)") title("B")

  Variables that uniquely identify margins: rat_MV_cat

. graph save fig2b.gph, replace
(note: file fig2b.gph not found)
(file fig2b.gph saved)

. 
. graph combine fig2a.gph fig2b.gph, ycommon xsize(6) ysize(3)

. 
. *********************
. **** Figure 3a/b  ***
. *********************
. 
. **** DUMMY Group Majority Treatment only: IA 
. xtlogit decisionprocedure i.gr_maj_pos##i.ind_util_pos i.period if treatment==2 , re vce(
> robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -545.42337  
Iteration 1:   log pseudolikelihood =  -489.4086  
Iteration 2:   log pseudolikelihood = -489.07029  
Iteration 3:   log pseudolikelihood = -489.07016  
Iteration 4:   log pseudolikelihood = -489.07016  

Fitting full model:

tau =  0.0     log pseudolikelihood = -489.07016
tau =  0.1     log pseudolikelihood = -485.21273
tau =  0.2     log pseudolikelihood = -483.66129
tau =  0.3     log pseudolikelihood = -483.84353

Iteration 0:   log pseudolikelihood = -483.66129  
Iteration 1:   log pseudolikelihood = -483.31678  
Iteration 2:   log pseudolikelihood = -483.30788  
Iteration 3:   log pseudolikelihood = -483.30788  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =        828
Group variable: id                              Number of groups  =         69

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(14)     =      37.99
Log pseudolikelihood  = -483.30788              Prob > chi2       =     0.0005

                                               (Std. Err. adjusted for 69 clusters in id)
-----------------------------------------------------------------------------------------
                        |               Robust
      decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
             gr_maj_pos |
                Pro PG  |  -1.512443   .3729331    -4.06   0.000    -2.243379   -.7815078
                        |
           ind_util_pos |
           Ind.U. Pos.  |  -1.816244   .3784183    -4.80   0.000     -2.55793   -1.074558
                        |
gr_maj_pos#ind_util_pos |
    Pro PG#Ind.U. Pos.  |    3.31884   .6118151     5.42   0.000     2.119704    4.517975
                        |
                 period |
                     2  |  -.1908915   .3714704    -0.51   0.607    -.9189601    .5371771
                     3  |   .3144819   .3839154     0.82   0.413    -.4379785    1.066942
                     4  |   .4249624   .4092591     1.04   0.299    -.3771707    1.227096
                     5  |   .4695513   .3821222     1.23   0.219    -.2793944    1.218497
                     6  |   .7924032   .4399423     1.80   0.072    -.0698678    1.654674
                     7  |   .5329276   .4290745     1.24   0.214    -.3080429    1.373898
                     8  |   .4349794   .3882438     1.12   0.263    -.3259645    1.195923
                     9  |   .6790432   .4182974     1.62   0.105    -.1408047    1.498891
                    10  |   .4939738   .4206159     1.17   0.240    -.3304183    1.318366
                    11  |   .3998443    .437622     0.91   0.361     -.457879    1.257568
                    12  |   .6571281   .3756068     1.75   0.080    -.0790477    1.393304
                        |
                  _cons |    .777389    .358849     2.17   0.030     .0740578     1.48072
------------------------+----------------------------------------------------------------
               /lnsig2u |  -1.098082   .4513954                     -1.982801   -.2133637
------------------------+----------------------------------------------------------------
                sigma_u |   .5775032   .1303412                      .3710566    .8988116
                    rho |   .0920439    .037724                      .0401695    .1971487
-----------------------------------------------------------------------------------------

. est store m3a

. margins  gr_maj_pos#i.ind_util_pos 

Predictive margins                              Number of obs     =        828
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)

-----------------------------------------------------------------------------------------
                        |            Delta-method
                        |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
gr_maj_pos#ind_util_pos |
 Contra PG#Ind.U. Neg.  |   .7503777   .0378736    19.81   0.000     .6761468    .8246086
 Contra PG#Ind.U. Pos.  |   .3614907   .0546612     6.61   0.000     .2543567    .4686247
    Pro PG#Ind.U. Neg.  |   .4280418   .0537556     7.96   0.000     .3226827    .5334009
    Pro PG#Ind.U. Pos.  |   .7486575   .0416129    17.99   0.000     .6670977    .8302172
-----------------------------------------------------------------------------------------

. marginsplot,  yline(.6361708, lpattern(solid)) yline(.575639 , lpattern(dash)) yline(.696
> 7027, lpattern(dash)) ytitle("Pr(MV)") title("A")

  Variables that uniquely identify margins: gr_maj_pos ind_util_pos

. graph save fig3a.gph, replace
(note: file fig3a.gph not found)
(file fig3a.gph saved)

. 
. *** DUMMY Group Benefit Treatment only: IA
. xtlogit decisionprocedure i.gr_util_pos##i.ind_util_pos i.period if treatment==3 , re vce
> (robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -374.16613  
Iteration 1:   log pseudolikelihood = -327.53011  
Iteration 2:   log pseudolikelihood = -327.45434  
Iteration 3:   log pseudolikelihood = -327.45433  

Fitting full model:

tau =  0.0     log pseudolikelihood = -327.45433
tau =  0.1     log pseudolikelihood = -322.53463
tau =  0.2     log pseudolikelihood = -319.71259
tau =  0.3     log pseudolikelihood = -318.36361
tau =  0.4     log pseudolikelihood = -318.19603
tau =  0.5     log pseudolikelihood =  -319.1439

Iteration 0:   log pseudolikelihood = -318.19399  
Iteration 1:   log pseudolikelihood =    -317.57  
Iteration 2:   log pseudolikelihood = -317.56915  
Iteration 3:   log pseudolikelihood = -317.56915  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =        540
Group variable: id                              Number of groups  =         45

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(14)     =      50.37
Log pseudolikelihood  = -317.56915              Prob > chi2       =     0.0000

                                                (Std. Err. adjusted for 45 clusters in id)
------------------------------------------------------------------------------------------
                         |               Robust
       decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
             gr_util_pos |
                   Pos.  |   2.482018   .5692061     4.36   0.000     1.366394    3.597641
                         |
            ind_util_pos |
            Ind.U. Pos.  |   2.159482   .4777052     4.52   0.000     1.223197    3.095767
                         |
gr_util_pos#ind_util_pos |
       Pos.#Ind.U. Pos.  |  -3.589254   .9190342    -3.91   0.000    -5.390528    -1.78798
                         |
                  period |
                      2  |  -.3461476   .5322393    -0.65   0.515    -1.389317    .6970222
                      3  |  -.5259638   .4643376    -1.13   0.257    -1.436049    .3841211
                      4  |  -.0504959   .4931442    -0.10   0.918    -1.017041     .916049
                      5  |   -.523812    .516269    -1.01   0.310    -1.535681    .4880567
                      6  |  -1.622972    .540168    -3.00   0.003    -2.681682   -.5642626
                      7  |   .2275433   .5010195     0.45   0.650    -.7544369    1.209524
                      8  |  -.3900784   .4844387    -0.81   0.421    -1.339561     .559404
                      9  |  -.7543081   .4946269    -1.53   0.127    -1.723759    .2151428
                     10  |  -.6713519   .5011374    -1.34   0.180    -1.653563    .3108593
                     11  |  -.5194362    .486897    -1.07   0.286    -1.473737    .4348644
                     12  |  -.9640279   .4707163    -2.05   0.041    -1.886615    -.041441
                         |
                   _cons |  -.8559691    .462603    -1.85   0.064    -1.762654    .0507161
-------------------------+----------------------------------------------------------------
                /lnsig2u |  -.4340521   .5616814                     -1.534927    .6668231
-------------------------+----------------------------------------------------------------
                 sigma_u |    .804909   .2260512                      .4641889    1.395722
                     rho |   .1645303   .0772088                      .0614695    .3719117
------------------------------------------------------------------------------------------

. est store m3b

. margins  gr_util_pos#i.ind_util_pos

Predictive margins                              Number of obs     =        540
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)

------------------------------------------------------------------------------------------
                         |            Delta-method
                         |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
gr_util_pos#ind_util_pos |
       Neg.#Ind.U. Neg.  |   .2374083   .0539327     4.40   0.000      .131702    .3431145
       Neg.#Ind.U. Pos.  |   .6623322   .0589851    11.23   0.000     .5467236    .7779408
       Pos.#Ind.U. Neg.  |   .7210942   .0505133    14.28   0.000       .62209    .8200985
       Pos.#Ind.U. Pos.  |    .434501   .0685102     6.34   0.000     .3002234    .5687785
------------------------------------------------------------------------------------------

. marginsplot, yline(.6361708, lpattern(solid)) yline(.575639 , lpattern(dash)) yline(.6967
> 027, lpattern(dash)) ytitle("Pr(MV)")  title("B")

  Variables that uniquely identify margins: gr_util_pos ind_util_pos

. graph save fig3b.gph, replace
(note: file fig3b.gph not found)
(file fig3b.gph saved)

. 
. graph combine fig3a.gph fig3b.gph, ycommon xsize(6) ysize(3)

. 
. *****************
. *** Table A6  ***
. *****************
. 
. esttab m1 m2a m2b m3a m3b  using tab_A6.csv, se(2) brackets star(* 0.10 ** 0.05 *** 0.01)
>  scalars("ll Log pseudolik.") aic bic nogaps replace label  nobaselevels
(note: file tab_A6.csv not found)
(output written to tab_A6.csv)

. 
. 
. ***********************
. **** PLACEBO TESTS  ***
. ***********************
. 
. *** Treatment dummies
. tab treatment, gen(treat_dum)

  Treatment |      Freq.     Percent        Cum.
------------+-----------------------------------
    No Info |        576       29.63       29.63
  Gr.Major. |        828       42.59       72.22
 Gr.Benefit |        540       27.78      100.00
------------+-----------------------------------
      Total |      1,944      100.00

. 
. *** Subsample Treatment 1 and 2
. gen treat12 = 0

. replace treat12 = 1 if treatment==1
(576 real changes made)

. replace treat12 = 1 if treatment==2
(828 real changes made)

. 
. *** Subsample Treatment 1 and 3
. gen treat13 = 0

. replace treat13 = 1 if treatment==1
(576 real changes made)

. replace treat13 = 1 if treatment==3
(540 real changes made)

. 
. tsset id period
       panel variable:  id (strongly balanced)
        time variable:  period, 1 to 12
                delta:  1 unit

. fvset base 1 treatment

. 
. *****************
. *** Figure A4 ***
. *****************
. 
. * A4a Model 2a (T2 vs T1) 
. xtlogit decisionprocedure i.rat_MVp1##i.treat_dum2        i.period if treat12==1 , re vce
> (robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -923.30314  
Iteration 1:   log pseudolikelihood = -861.65542  
Iteration 2:   log pseudolikelihood = -861.33335  
Iteration 3:   log pseudolikelihood = -861.33327  

Fitting full model:

tau =  0.0     log pseudolikelihood = -861.33327
tau =  0.1     log pseudolikelihood = -849.76605
tau =  0.2     log pseudolikelihood = -843.64962
tau =  0.3     log pseudolikelihood = -841.32728
tau =  0.4     log pseudolikelihood = -842.02818

Iteration 0:   log pseudolikelihood = -841.32722  
Iteration 1:   log pseudolikelihood = -840.65755  
Iteration 2:   log pseudolikelihood = -840.65548  
Iteration 3:   log pseudolikelihood = -840.65548  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,404
Group variable: id                              Number of groups  =        117

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(14)     =      48.13
Log pseudolikelihood  = -840.65548              Prob > chi2       =     0.0000

                                          (Std. Err. adjusted for 117 clusters in id)
-------------------------------------------------------------------------------------
                    |               Robust
  decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
           rat_MVp1 |
                MV  |   .4567401   .1991617     2.29   0.022     .0663902    .8470899
       1.treat_dum2 |  -.7992063   .2686562    -2.97   0.003    -1.325763   -.2726498
                    |
rat_MVp1#treat_dum2 |
              MV#1  |   1.234195   .3699325     3.34   0.001     .5091402    1.959249
                    |
             period |
                 2  |  -.2505407   .2953209    -0.85   0.396    -.8293591    .3282777
                 3  |    .204774   .3049975     0.67   0.502    -.3930101    .8025581
                 4  |   .6044967   .3372605     1.79   0.073    -.0565218    1.265515
                 5  |   .4239906   .3104263     1.37   0.172    -.1844338    1.032415
                 6  |   .4301426   .3126914     1.38   0.169    -.1827212    1.043007
                 7  |   .4634766   .3232318     1.43   0.152    -.1700462    1.096999
                 8  |    .338944    .294868     1.15   0.250    -.2389867    .9168747
                 9  |    .521534   .2927587     1.78   0.075    -.0522625    1.095331
                10  |   .7415184   .3323564     2.23   0.026     .0901118    1.392925
                11  |   .6586699    .324675     2.03   0.042     .0223185    1.295021
                12  |   .5135906   .2973546     1.73   0.084    -.0692137    1.096395
                    |
              _cons |  -.0610942    .268815    -0.23   0.820    -.5879618    .4657735
--------------------+----------------------------------------------------------------
           /lnsig2u |  -.6812121   .2857698                     -1.241311   -.1211137
--------------------+----------------------------------------------------------------
            sigma_u |   .7113391   .1016396                       .537592    .9412403
                rho |   .1333036   .0330161                      .0807531    .2121589
-------------------------------------------------------------------------------------

. est store m2a_p1 

. margins i.rat_MVp1, dydx(i.treat_dum2) post

Average marginal effects                        Number of obs     =      1,404
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.treat_dum2

-------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
0.treat_dum2  |  (base outcome)
--------------+----------------------------------------------------------------
1.treat_dum2  |
     rat_MVp1 |
    Delegate  |  -.1751252   .0577386    -3.03   0.002    -.2882906   -.0619597
          MV  |   .0804881    .046708     1.72   0.085    -.0110579    .1720341
-------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0)  ytitle("Effects on Pr(MV)") xtitle(" ") title("A") 

  Variables that uniquely identify margins: rat_MVp1

. graph save fig4a.gph, replace
(note: file fig4a.gph not found)
(file fig4a.gph saved)

. * Model 2b (T2 vs T1)
. xtlogit decisionprocedure c.rat_MV_catp1##i.treat_dum2       i.period if treat12==1 , re 
> vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -923.30314  
Iteration 1:   log pseudolikelihood = -858.75428  
Iteration 2:   log pseudolikelihood = -858.48091  
Iteration 3:   log pseudolikelihood = -858.48084  

Fitting full model:

tau =  0.0     log pseudolikelihood = -858.48084
tau =  0.1     log pseudolikelihood = -846.55048
tau =  0.2     log pseudolikelihood = -840.07251
tau =  0.3     log pseudolikelihood = -837.41134
tau =  0.4     log pseudolikelihood = -837.79647

Iteration 0:   log pseudolikelihood = -837.41133  
Iteration 1:   log pseudolikelihood =  -836.5184  
Iteration 2:   log pseudolikelihood = -836.51359  
Iteration 3:   log pseudolikelihood = -836.51359  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,404
Group variable: id                              Number of groups  =        117

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(14)     =      54.25
Log pseudolikelihood  = -836.51359              Prob > chi2       =     0.0000

                                        (Std. Err. adjusted for 117 clusters in id)
-----------------------------------------------------------------------------------
                  |               Robust
decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
     rat_MV_catp1 |   .2111511   .0586161     3.60   0.000     .0962656    .3260366
     1.treat_dum2 |   .0490994   .2021863     0.24   0.808    -.3471785    .4453773
                  |
       treat_dum2#|
   c.rat_MV_catp1 |
               1  |   .1980099   .0955431     2.07   0.038     .0107488     .385271
                  |
           period |
               2  |  -.1519221    .296412    -0.51   0.608    -.7328789    .4290347
               3  |   .3095476   .3024647     1.02   0.306    -.2832724    .9023676
               4  |   .5864226   .3346055     1.75   0.080    -.0693922    1.242237
               5  |   .4150271   .3025335     1.37   0.170    -.1779277    1.007982
               6  |   .4951458    .310599     1.59   0.111     -.113617    1.103909
               7  |   .5028448   .3153425     1.59   0.111    -.1152152    1.120905
               8  |   .4103767   .2923636     1.40   0.160    -.1626455     .983399
               9  |   .6368729     .29804     2.14   0.033     .0527251    1.221021
              10  |   .9439144   .3394672     2.78   0.005      .278571    1.609258
              11  |   .7233417   .3239495     2.23   0.026     .0884123    1.358271
              12  |   .6299901   .2960134     2.13   0.033     .0498144    1.210166
                  |
            _cons |   .2402015    .239272     1.00   0.315     -.228763     .709166
------------------+----------------------------------------------------------------
         /lnsig2u |  -.6216077   .2812867                      -1.17292   -.0702958
------------------+----------------------------------------------------------------
          sigma_u |   .7328576   .1030716                      .5562932    .9654626
              rho |   .1403417   .0339361                      .0859777    .2207771
-----------------------------------------------------------------------------------

. est store m2b_p1 

. margins, dydx(treat_dum2) at(rat_MV_catp1=(-4, -1.5, 1)) vsquish

Average marginal effects                        Number of obs     =      1,404
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.treat_dum2
1._at        : rat_MV_catp1    =          -4
2._at        : rat_MV_catp1    =        -1.5
3._at        : rat_MV_catp1    =           1

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
0.treat_dum2 |  (base outcome)
-------------+----------------------------------------------------------------
1.treat_dum2 |
         _at |
          1  |  -.1547935   .0744882    -2.08   0.038    -.3007877   -.0087994
          2  |   -.053795   .0441102    -1.22   0.223    -.1402493    .0326593
          3  |    .045087   .0460583     0.98   0.328    -.0451855    .1353595
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0) ytitle("Effects on Pr(MV)")  xtitle("EU(MV)") title("B")

  Variables that uniquely identify margins: rat_MV_catp1

. graph save fig4b.gph, replace
(note: file fig4b.gph not found)
(file fig4b.gph saved)

. graph combine fig4a.gph fig4b.gph, ycommon xsize(6) ysize(3)

. 
. *****************
. *** Figure A5 ***
. *****************
. 
. * A5a Model 2a (T3 vs T1) 
. xtlogit decisionprocedure i.rat_MVp2##i.treat_dum3        i.period if treat13==1 , re vce
> (robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -760.85889  
Iteration 1:   log pseudolikelihood = -700.55934  
Iteration 2:   log pseudolikelihood = -700.33954  
Iteration 3:   log pseudolikelihood = -700.33949  

Fitting full model:

tau =  0.0     log pseudolikelihood = -700.33949
tau =  0.1     log pseudolikelihood = -687.83067
tau =  0.2     log pseudolikelihood = -680.53102
tau =  0.3     log pseudolikelihood = -676.74719
tau =  0.4     log pseudolikelihood = -675.67594
tau =  0.5     log pseudolikelihood =  -677.0621

Iteration 0:   log pseudolikelihood = -675.67344  
Iteration 1:   log pseudolikelihood =  -674.8088  
Iteration 2:   log pseudolikelihood = -674.80741  
Iteration 3:   log pseudolikelihood = -674.80741  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,116
Group variable: id                              Number of groups  =         93

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(14)     =      62.15
Log pseudolikelihood  = -674.80741              Prob > chi2       =     0.0000

                                           (Std. Err. adjusted for 93 clusters in id)
-------------------------------------------------------------------------------------
                    |               Robust
  decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
           rat_MVp2 |
                MV  |   .7436987   .1922604     3.87   0.000     .3668752    1.120522
       1.treat_dum3 |  -1.109983   .3297743    -3.37   0.001    -1.756329   -.4636373
                    |
rat_MVp2#treat_dum3 |
              MV#1  |   1.029573   .4939141     2.08   0.037     .0615189    1.997626
                    |
             period |
                 2  |  -.0615333   .3693687    -0.17   0.868    -.7854826    .6624161
                 3  |    .220826   .3666003     0.60   0.547    -.4976974    .9393493
                 4  |    .568685   .3750402     1.52   0.129    -.1663802     1.30375
                 5  |   .2311977   .3747282     0.62   0.537     -.503256    .9656514
                 6  |  -.3951286   .3545187    -1.11   0.265    -1.089972    .2997152
                 7  |   .4060305   .3600566     1.13   0.259    -.2996675    1.111728
                 8  |   .1112053   .3218757     0.35   0.730    -.5196595      .74207
                 9  |   .1284568   .3359066     0.38   0.702    -.5299079    .7868216
                10  |   .4631018   .3610489     1.28   0.200    -.2445411    1.170745
                11  |   .8176687   .3592319     2.28   0.023     .1135871     1.52175
                12  |  -.0351666   .3421777    -0.10   0.918    -.7058224    .6354893
                    |
              _cons |    .077285   .2851634     0.27   0.786    -.4816251    .6361951
--------------------+----------------------------------------------------------------
           /lnsig2u |  -.3641795   .3217111                     -.9947216    .2663625
--------------------+----------------------------------------------------------------
            sigma_u |   .8335265   .1340773                      .6081335    1.142457
                rho |   .1743614   .0463134                      .1010539    .2840449
-------------------------------------------------------------------------------------

. est store m2a_p2 

. margins i.rat_MVp2, dydx(i.treat_dum3) post

Average marginal effects                        Number of obs     =      1,116
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.treat_dum3

-------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
0.treat_dum3  |  (base outcome)
--------------+----------------------------------------------------------------
1.treat_dum3  |
     rat_MVp2 |
    Delegate  |  -.2303376   .0651112    -3.54   0.000    -.3579532    -.102722
          MV  |  -.0146773   .0612971    -0.24   0.811    -.1348174    .1054628
-------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0) ytitle("Effects on Pr(MV)") xtitle(" ") title("A")

  Variables that uniquely identify margins: rat_MVp2

. graph save fig5a.gph, replace
(note: file fig5a.gph not found)
(file fig5a.gph saved)

. * A5b Model 2b (T3 vs T1)
. xtlogit decisionprocedure c.rat_MV_catp2##i.treat_dum3       i.period if treat13==1 , re 
> vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -760.85889  
Iteration 1:   log pseudolikelihood = -696.94201  
Iteration 2:   log pseudolikelihood = -696.70395  
Iteration 3:   log pseudolikelihood = -696.70389  

Fitting full model:

tau =  0.0     log pseudolikelihood = -696.70389
tau =  0.1     log pseudolikelihood = -684.08613
tau =  0.2     log pseudolikelihood = -676.65174
tau =  0.3     log pseudolikelihood = -672.73549
tau =  0.4     log pseudolikelihood = -671.54087
tau =  0.5     log pseudolikelihood = -672.81466

Iteration 0:   log pseudolikelihood = -671.53831  
Iteration 1:   log pseudolikelihood = -670.58219  
Iteration 2:   log pseudolikelihood = -670.58047  
Iteration 3:   log pseudolikelihood = -670.58047  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,116
Group variable: id                              Number of groups  =         93

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(14)     =      66.34
Log pseudolikelihood  = -670.58047              Prob > chi2       =     0.0000

                                         (Std. Err. adjusted for 93 clusters in id)
-----------------------------------------------------------------------------------
                  |               Robust
decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
     rat_MV_catp2 |   .2828844   .0664763     4.26   0.000     .1525933    .4131756
     1.treat_dum3 |   -.714722   .2331293    -3.07   0.002    -1.171647    -.257797
                  |
       treat_dum3#|
   c.rat_MV_catp2 |
               1  |   .2530341   .1493763     1.69   0.090     -.039738    .5458062
                  |
           period |
               2  |  -.1538579    .370362    -0.42   0.678     -.879754    .5720381
               3  |   .2075759   .3683296     0.56   0.573    -.5143369    .9294888
               4  |   .5245183   .3761207     1.39   0.163    -.2126647    1.261701
               5  |   .1054882   .3716588     0.28   0.777    -.6229496     .833926
               6  |  -.4523992   .3535742    -1.28   0.201    -1.145392    .2405935
               7  |   .3942329   .3637267     1.08   0.278    -.3186583    1.107124
               8  |   .2047837   .3311511     0.62   0.536    -.4442605     .853828
               9  |   .1883361   .3465513     0.54   0.587     -.490892    .8675642
              10  |   .4441914   .3674429     1.21   0.227    -.2759834    1.164366
              11  |   .7631695   .3627166     2.10   0.035      .052258    1.474081
              12  |   .0190136   .3524278     0.05   0.957    -.6717322    .7097594
                  |
            _cons |   .3585146   .2713018     1.32   0.186    -.1732273    .8902564
------------------+----------------------------------------------------------------
         /lnsig2u |  -.3365759   .3182262                     -.9602878    .2871361
------------------+----------------------------------------------------------------
          sigma_u |   .8451105   .1344682                      .6186943    1.154385
              rho |    .178371   .0466376                      .1042252    .2882884
-----------------------------------------------------------------------------------

. est store m2b_p2 

. margins, dydx(treat_dum3) at(rat_MV_catp2=(-2, -.75, 2)) vsquish

Average marginal effects                        Number of obs     =      1,116
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.treat_dum3
1._at        : rat_MV_catp2    =          -2
2._at        : rat_MV_catp2    =        -.75
3._at        : rat_MV_catp2    =           2

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
0.treat_dum3 |  (base outcome)
-------------+----------------------------------------------------------------
1.treat_dum3 |
         _at |
          1  |  -.2396422   .0760417    -3.15   0.002    -.3886811   -.0906032
          2  |  -.1899982   .0583798    -3.25   0.001    -.3044204   -.0755759
          3  |  -.0377264   .0594592    -0.63   0.526    -.1542644    .0788116
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0) ytitle("Effects on Pr(MV)")  xtitle("EU(MV)") title("B")

  Variables that uniquely identify margins: rat_MV_catp2

. graph save fig5b, replace
(note: file fig5b.gph not found)
(file fig5b.gph saved)

. graph combine fig5a.gph fig5b.gph, ycommon xsize(6) ysize(3)

. 
. 
. *****************
. *** Figure A6 ***
. *****************
. 
. * A6a1
. xtlogit decisionprocedure i.gr_maj_pos##i.ind_util_pos##i.treat_dum2 i.period if treat12=
> =1 , re vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -923.30314  
Iteration 1:   log pseudolikelihood = -856.77637  
Iteration 2:   log pseudolikelihood = -856.43219  
Iteration 3:   log pseudolikelihood = -856.43211  

Fitting full model:

tau =  0.0     log pseudolikelihood = -856.43211
tau =  0.1     log pseudolikelihood = -844.83837
tau =  0.2     log pseudolikelihood = -838.64353
tau =  0.3     log pseudolikelihood =  -836.2312
tau =  0.4     log pseudolikelihood = -836.84379

Iteration 0:   log pseudolikelihood = -836.23112  
Iteration 1:   log pseudolikelihood = -835.46122  
Iteration 2:   log pseudolikelihood = -835.45845  
Iteration 3:   log pseudolikelihood = -835.45845  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,404
Group variable: id                              Number of groups  =        117

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(18)     =      56.13
Log pseudolikelihood  = -835.45845              Prob > chi2       =     0.0000

                                               (Std. Err. adjusted for 117 clusters in id)
------------------------------------------------------------------------------------------
                         |               Robust
       decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
              gr_maj_pos |
                 Pro PG  |  -.4146855   .2891782    -1.43   0.152    -.9814643    .1520934
                         |
            ind_util_pos |
            Ind.U. Pos.  |   .0979778   .3053984     0.32   0.748    -.5005922    .6965477
                         |
 gr_maj_pos#ind_util_pos |
     Pro PG#Ind.U. Pos.  |    .931909   .4041625     2.31   0.021      .139765    1.724053
                         |
            1.treat_dum2 |    .740097   .2999965     2.47   0.014     .1521146    1.328079
                         |
   gr_maj_pos#treat_dum2 |
               Pro PG#1  |  -1.152906   .4609513    -2.50   0.012    -2.056354   -.2494577
                         |
 ind_util_pos#treat_dum2 |
          Ind.U. Pos.#1  |   -1.94062      .4936    -3.93   0.000    -2.908058    -.973182
                         |
 gr_maj_pos#ind_util_pos#|
              treat_dum2 |
   Pro PG#Ind.U. Pos.#1  |   2.456647    .746367     3.29   0.001     .9937942    3.919499
                         |
                  period |
                      2  |  -.1898994   .3019496    -0.63   0.529    -.7817098    .4019109
                      3  |   .2196381   .3145741     0.70   0.485    -.3969159     .836192
                      4  |   .6053615   .3363392     1.80   0.072    -.0538512    1.264574
                      5  |   .4044551   .3006736     1.35   0.179    -.1848544    .9937646
                      6  |   .4922147   .3215769     1.53   0.126    -.1380644    1.122494
                      7  |   .4344435   .3323525     1.31   0.191    -.2169555    1.085842
                      8  |   .2890604   .3064222     0.94   0.346     -.311516    .8896368
                      9  |   .5617582   .3024584     1.86   0.063    -.0310494    1.154566
                     10  |   .7823768   .3333936     2.35   0.019     .1289374    1.435816
                     11  |   .6815448   .3287522     2.07   0.038     .0372023    1.325887
                     12  |   .4677824   .3083448     1.52   0.129    -.1365622    1.072127
                         |
                   _cons |   .0943363   .2602248     0.36   0.717     -.415695    .6043676
-------------------------+----------------------------------------------------------------
                /lnsig2u |  -.6608179   .2803026                     -1.210201   -.1114348
-------------------------+----------------------------------------------------------------
                 sigma_u |   .7186298   .1007169                      .5460196    .9458064
                     rho |   .1356775   .0328708                      .0830928    .2137812
------------------------------------------------------------------------------------------

. est store m3a_p 

. margins gr_maj_pos, dydx(ind_util_pos) at(treat_dum2==1) post

Average marginal effects                        Number of obs     =      1,404
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.ind_util_pos
at           : treat_dum2      =           1

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
0.ind_util_pos  |  (base outcome)
----------------+----------------------------------------------------------------
1.ind_util_pos  |
     gr_maj_pos |
     Contra PG  |  -.3819309   .0731135    -5.22   0.000    -.5252307   -.2386311
        Pro PG  |   .3198583   .0693089     4.61   0.000     .1840153    .4557014
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0) ytitle("Effects on Pr(MV)") title("A1")

  Variables that uniquely identify margins: gr_maj_pos

. graph save fig6a1.gph, replace
(note: file fig6a1.gph not found)
(file fig6a1.gph saved)

. * A6a2
. xtlogit decisionprocedure i.gr_maj_pos##i.ind_util_pos##i.treat_dum2 i.period if treat12=
> =1 , re vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -923.30314  
Iteration 1:   log pseudolikelihood = -856.77637  
Iteration 2:   log pseudolikelihood = -856.43219  
Iteration 3:   log pseudolikelihood = -856.43211  

Fitting full model:

tau =  0.0     log pseudolikelihood = -856.43211
tau =  0.1     log pseudolikelihood = -844.83837
tau =  0.2     log pseudolikelihood = -838.64353
tau =  0.3     log pseudolikelihood =  -836.2312
tau =  0.4     log pseudolikelihood = -836.84379

Iteration 0:   log pseudolikelihood = -836.23112  
Iteration 1:   log pseudolikelihood = -835.46122  
Iteration 2:   log pseudolikelihood = -835.45845  
Iteration 3:   log pseudolikelihood = -835.45845  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,404
Group variable: id                              Number of groups  =        117

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(18)     =      56.13
Log pseudolikelihood  = -835.45845              Prob > chi2       =     0.0000

                                               (Std. Err. adjusted for 117 clusters in id)
------------------------------------------------------------------------------------------
                         |               Robust
       decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
              gr_maj_pos |
                 Pro PG  |  -.4146855   .2891782    -1.43   0.152    -.9814643    .1520934
                         |
            ind_util_pos |
            Ind.U. Pos.  |   .0979778   .3053984     0.32   0.748    -.5005922    .6965477
                         |
 gr_maj_pos#ind_util_pos |
     Pro PG#Ind.U. Pos.  |    .931909   .4041625     2.31   0.021      .139765    1.724053
                         |
            1.treat_dum2 |    .740097   .2999965     2.47   0.014     .1521146    1.328079
                         |
   gr_maj_pos#treat_dum2 |
               Pro PG#1  |  -1.152906   .4609513    -2.50   0.012    -2.056354   -.2494577
                         |
 ind_util_pos#treat_dum2 |
          Ind.U. Pos.#1  |   -1.94062      .4936    -3.93   0.000    -2.908058    -.973182
                         |
 gr_maj_pos#ind_util_pos#|
              treat_dum2 |
   Pro PG#Ind.U. Pos.#1  |   2.456647    .746367     3.29   0.001     .9937942    3.919499
                         |
                  period |
                      2  |  -.1898994   .3019496    -0.63   0.529    -.7817098    .4019109
                      3  |   .2196381   .3145741     0.70   0.485    -.3969159     .836192
                      4  |   .6053615   .3363392     1.80   0.072    -.0538512    1.264574
                      5  |   .4044551   .3006736     1.35   0.179    -.1848544    .9937646
                      6  |   .4922147   .3215769     1.53   0.126    -.1380644    1.122494
                      7  |   .4344435   .3323525     1.31   0.191    -.2169555    1.085842
                      8  |   .2890604   .3064222     0.94   0.346     -.311516    .8896368
                      9  |   .5617582   .3024584     1.86   0.063    -.0310494    1.154566
                     10  |   .7823768   .3333936     2.35   0.019     .1289374    1.435816
                     11  |   .6815448   .3287522     2.07   0.038     .0372023    1.325887
                     12  |   .4677824   .3083448     1.52   0.129    -.1365622    1.072127
                         |
                   _cons |   .0943363   .2602248     0.36   0.717     -.415695    .6043676
-------------------------+----------------------------------------------------------------
                /lnsig2u |  -.6608179   .2803026                     -1.210201   -.1114348
-------------------------+----------------------------------------------------------------
                 sigma_u |   .7186298   .1007169                      .5460196    .9458064
                     rho |   .1356775   .0328708                      .0830928    .2137812
------------------------------------------------------------------------------------------

. margins gr_maj_pos, dydx(ind_util_pos) at(treat_dum2==0) post

Average marginal effects                        Number of obs     =      1,404
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.ind_util_pos
at           : treat_dum2      =           0

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
0.ind_util_pos  |  (base outcome)
----------------+----------------------------------------------------------------
1.ind_util_pos  |
     gr_maj_pos |
     Contra PG  |   .0205535   .0639564     0.32   0.748    -.1047988    .1459057
        Pro PG  |    .211063   .0617118     3.42   0.001     .0901101    .3320159
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0) ytitle("Effects on Pr(MV)") title("A2")

  Variables that uniquely identify margins: gr_maj_pos

. graph save fig6a2.gph, replace
(note: file fig6a2.gph not found)
(file fig6a2.gph saved)

. graph combine fig6a1.gph fig6a2.gph, ycommon xsize(6) ysize(3)

. 
. *****************
. *** Figure A7 ***
. *****************
. 
. * A7b1
. xtlogit decisionprocedure i.gr_util_pos##i.ind_util_pos##i.treat_dum3 i.period if treat13
> ==1 , re vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -760.85889  
Iteration 1:   log pseudolikelihood = -693.80546  
Iteration 2:   log pseudolikelihood = -693.49762  
Iteration 3:   log pseudolikelihood = -693.49751  
Iteration 4:   log pseudolikelihood = -693.49751  

Fitting full model:

tau =  0.0     log pseudolikelihood = -693.49751
tau =  0.1     log pseudolikelihood = -680.80039
tau =  0.2     log pseudolikelihood = -673.28155
tau =  0.3     log pseudolikelihood = -669.28397
tau =  0.4     log pseudolikelihood = -668.01373
tau =  0.5     log pseudolikelihood = -669.21652

Iteration 0:   log pseudolikelihood = -668.01115  
Iteration 1:   log pseudolikelihood = -667.01717  
Iteration 2:   log pseudolikelihood = -667.01514  
Iteration 3:   log pseudolikelihood = -667.01514  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,116
Group variable: id                              Number of groups  =         93

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(18)     =      90.15
Log pseudolikelihood  = -667.01514              Prob > chi2       =     0.0000

                                                (Std. Err. adjusted for 93 clusters in id)
------------------------------------------------------------------------------------------
                         |               Robust
       decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
             gr_util_pos |
                   Pos.  |   .8215436   .2409774     3.41   0.001     .3492366    1.293851
                         |
            ind_util_pos |
            Ind.U. Pos.  |    1.34293   .3070283     4.37   0.000     .7411659    1.944695
                         |
gr_util_pos#ind_util_pos |
       Pos.#Ind.U. Pos.  |  -1.514117   .3928327    -3.85   0.000    -2.284055   -.7441788
                         |
            1.treat_dum3 |  -1.175666   .3791084    -3.10   0.002    -1.918705    -.432627
                         |
  gr_util_pos#treat_dum3 |
                 Pos.#1  |   1.348098    .606481     2.22   0.026     .1594171    2.536779
                         |
 ind_util_pos#treat_dum3 |
          Ind.U. Pos.#1  |   .8118755   .5666111     1.43   0.152    -.2986618    1.922413
                         |
             gr_util_pos#|
 ind_util_pos#treat_dum3 |
     Pos.#Ind.U. Pos.#1  |   -2.07022   1.004416    -2.06   0.039    -4.038839   -.1016014
                         |
                  period |
                      2  |  -.1043956   .3704471    -0.28   0.778    -.8304586    .6216675
                      3  |   .0218154   .3868321     0.06   0.955    -.7363615    .7799923
                      4  |   .5942367   .3947729     1.51   0.132     -.179504    1.367977
                      5  |   .1567896   .3827584     0.41   0.682    -.5934031    .9069822
                      6  |  -.5495955     .37939    -1.45   0.147    -1.293186    .1939953
                      7  |   .3721064   .3785842     0.98   0.326     -.369905    1.114118
                      8  |    .006187   .3496898     0.02   0.986    -.6791924    .6915664
                      9  |   .0677299   .3570431     0.19   0.850    -.6320617    .7675215
                     10  |   .4693062   .3854927     1.22   0.223    -.2862456    1.224858
                     11  |   .6300981   .3863798     1.63   0.103    -.1271925    1.387389
                     12  |  -.1725177   .3652444    -0.47   0.637    -.8883835     .543348
                         |
                   _cons |  -.1596747   .2918481    -0.55   0.584    -.7316864     .412337
-------------------------+----------------------------------------------------------------
                /lnsig2u |  -.3217085    .315391                     -.9398634    .2964465
-------------------------+----------------------------------------------------------------
                 sigma_u |   .8514162   .1342645                       .625045    1.159772
                     rho |   .1805603   .0466647                      .1061475    .2902024
------------------------------------------------------------------------------------------

. est store m3b_p 

. margins gr_util_pos, dydx(ind_util_pos) at(treat_dum3==1) post

Average marginal effects                        Number of obs     =      1,116
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.ind_util_pos
at           : treat_dum3      =           1

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
0.ind_util_pos  |  (base outcome)
----------------+----------------------------------------------------------------
1.ind_util_pos  |
    gr_util_pos |
          Neg.  |   .4291893   .0840138     5.11   0.000     .2645252    .5938534
          Pos.  |  -.2924228   .0962141    -3.04   0.002    -.4809989   -.1038467
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0) ytitle("Effects on Pr(MV)") title("B1")

  Variables that uniquely identify margins: gr_util_pos

. graph save fig7b1.gph, replace
(note: file fig7b1.gph not found)
(file fig7b1.gph saved)

. xtlogit decisionprocedure i.gr_util_pos##i.ind_util_pos##i.treat_dum3 i.period if treat13
> ==1 , re vce(robust)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -760.85889  
Iteration 1:   log pseudolikelihood = -693.80546  
Iteration 2:   log pseudolikelihood = -693.49762  
Iteration 3:   log pseudolikelihood = -693.49751  
Iteration 4:   log pseudolikelihood = -693.49751  

Fitting full model:

tau =  0.0     log pseudolikelihood = -693.49751
tau =  0.1     log pseudolikelihood = -680.80039
tau =  0.2     log pseudolikelihood = -673.28155
tau =  0.3     log pseudolikelihood = -669.28397
tau =  0.4     log pseudolikelihood = -668.01373
tau =  0.5     log pseudolikelihood = -669.21652

Iteration 0:   log pseudolikelihood = -668.01115  
Iteration 1:   log pseudolikelihood = -667.01717  
Iteration 2:   log pseudolikelihood = -667.01514  
Iteration 3:   log pseudolikelihood = -667.01514  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =      1,116
Group variable: id                              Number of groups  =         93

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         12
                                                              avg =       12.0
                                                              max =         12

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(18)     =      90.15
Log pseudolikelihood  = -667.01514              Prob > chi2       =     0.0000

                                                (Std. Err. adjusted for 93 clusters in id)
------------------------------------------------------------------------------------------
                         |               Robust
       decisionprocedure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
             gr_util_pos |
                   Pos.  |   .8215436   .2409774     3.41   0.001     .3492366    1.293851
                         |
            ind_util_pos |
            Ind.U. Pos.  |    1.34293   .3070283     4.37   0.000     .7411659    1.944695
                         |
gr_util_pos#ind_util_pos |
       Pos.#Ind.U. Pos.  |  -1.514117   .3928327    -3.85   0.000    -2.284055   -.7441788
                         |
            1.treat_dum3 |  -1.175666   .3791084    -3.10   0.002    -1.918705    -.432627
                         |
  gr_util_pos#treat_dum3 |
                 Pos.#1  |   1.348098    .606481     2.22   0.026     .1594171    2.536779
                         |
 ind_util_pos#treat_dum3 |
          Ind.U. Pos.#1  |   .8118755   .5666111     1.43   0.152    -.2986618    1.922413
                         |
             gr_util_pos#|
 ind_util_pos#treat_dum3 |
     Pos.#Ind.U. Pos.#1  |   -2.07022   1.004416    -2.06   0.039    -4.038839   -.1016014
                         |
                  period |
                      2  |  -.1043956   .3704471    -0.28   0.778    -.8304586    .6216675
                      3  |   .0218154   .3868321     0.06   0.955    -.7363615    .7799923
                      4  |   .5942367   .3947729     1.51   0.132     -.179504    1.367977
                      5  |   .1567896   .3827584     0.41   0.682    -.5934031    .9069822
                      6  |  -.5495955     .37939    -1.45   0.147    -1.293186    .1939953
                      7  |   .3721064   .3785842     0.98   0.326     -.369905    1.114118
                      8  |    .006187   .3496898     0.02   0.986    -.6791924    .6915664
                      9  |   .0677299   .3570431     0.19   0.850    -.6320617    .7675215
                     10  |   .4693062   .3854927     1.22   0.223    -.2862456    1.224858
                     11  |   .6300981   .3863798     1.63   0.103    -.1271925    1.387389
                     12  |  -.1725177   .3652444    -0.47   0.637    -.8883835     .543348
                         |
                   _cons |  -.1596747   .2918481    -0.55   0.584    -.7316864     .412337
-------------------------+----------------------------------------------------------------
                /lnsig2u |  -.3217085    .315391                     -.9398634    .2964465
-------------------------+----------------------------------------------------------------
                 sigma_u |   .8514162   .1342645                       .625045    1.159772
                     rho |   .1805603   .0466647                      .1061475    .2902024
------------------------------------------------------------------------------------------

. * A7b2
. margins gr_util_pos, dydx(ind_util_pos) at(treat_dum3==0) post

Average marginal effects                        Number of obs     =      1,116
Model VCE    : Robust

Expression   : Pr(decisionprocedure=1), predict(pr)
dy/dx w.r.t. : 1.ind_util_pos
at           : treat_dum3      =           0

---------------------------------------------------------------------------------
                |            Delta-method
                |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
0.ind_util_pos  |  (base outcome)
----------------+----------------------------------------------------------------
1.ind_util_pos  |
    gr_util_pos |
          Neg.  |   .2615484   .0544427     4.80   0.000     .1548427     .368254
          Pos.  |  -.0335446   .0605759    -0.55   0.580    -.1522713     .085182
---------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. marginsplot, yline(0) ytitle("Effects on Pr(MV)") title("B2")

  Variables that uniquely identify margins: gr_util_pos

. graph save fig7b2.gph, replace
(note: file fig7b2.gph not found)
(file fig7b2.gph saved)

. graph combine fig7b1.gph fig7b2.gph, ycommon xsize(6) ysize(3)

. 
. *****************
. *** Table A6  ***
. *****************
. 
. esttab m2a_p1 m2b_p1 m2a_p2 m2b_p2 m3a_p m3b_p using tab_A7.csv, se(2) brackets star(* 0.
> 10 ** 0.05 *** 0.01) scalars("ll Log pseudolik.") aic bic nogaps replace label  nobaselev
> els
(note: file tab_A7.csv not found)
(output written to tab_A7.csv)

. 
. log close
      name:  <unnamed>
       log:  ~\PG_DataFile\pg_log.log
  log type:  text
 closed on:   1 Apr 2021, 23:22:31
-------------------------------------------------------------------------------------------
